One of the first things that boxers learn is to keep their hands at eye level when they fight. As they progress through the rounds, their hands drop to chin level, and they need a reminder to raise them again. This is important because they are ready to throw a punch at the opportune time while defending their faces.
Boxers touch their noses to remember to keep their hands in the proper position. By touching their nose, they need to raise their hands back up to eye level, and they will keep their hands in the right position. Also, it provides boxers with an opportunity to reset and refocus as they prepare for the next round.